A bias written in a story, either intentionally or unintentionally is powerful. If done consciously as a character’s trait, an author should try to integrate that bias into the narrative - if done seamlessly, the reader will accept the character and will continue reading the story.
If a character’s bias becomes the defining trait that overwhelms everything else, the author runs the risk of turning off their readers. A bias, for bias’ sake usually ends up being this overwhelming nature just because a “natural” bias is a part of the character but not the determinate of said character.
The characters in To Kill a Mockingbird exhibited bias but readers, even today, still enjoy the book because the story is not solely defined by that bias.
Bias’ effect on your reader has nothing to do with the genre you are writing because bias affects everyone in different ways. Cat lovers may not like that your character hates cats but they can still love the character if you write a more in-depth character. If all they see in your character is that she hates cats then cat lovers might not be able to read your story. I hope this conveys what I’m trying to say; articulation is sometimes elusive to me.